Book review: The Theory That Would Not Die

A few months ago, Autonomy founder and CEO Mike Lynch sold his company to HP for £7.1 billion. Back in 2000, when he had just become Britain's first software billionaire, Lynch gave an interview in which he talked about perception and explained how he built his company. It was based, he said, on the ideas of a little-known 18th-century clergyman called Thomas Bayes. That was my introduction to Thomas Bayes, whose ideas have been used to solve many intractable problems, a number of which Sharon Bertsch McGrayne studies in depth in The Theory That Would Not Die.

In the last ten years, Bayes has become famous, and few working in the field of probability theory, computer intelligence or mathematics can have failed to have come into contact with his rule. In fact, you have only to look at your spam filter to see Bayes in action. Many now take his ideas — without necessarily understanding them — so much for granted that they're surprised to learn that for two and a half centuries openly endorsing Bayes was career suicide. During that time Bayesians hid; his ideas survived in little pockets, neither quite dying out nor gaining wide adoption.

One such pocket was Bletchley Park, where during World War II Alan Turing developed his own version of Bayes as part of his work on the Enigma machine. That ought to have been the moment when the power of Bayes was finally fully appreciated. That didn't happen, because after the war everything related to the decryption efforts remained classified — Churchill even ordered the destruction of all the evidence. The opportunity cost to the nation of those decisions can't reliably be calculated: imagine if Turing's achievements had been celebrated and the nation's science and technology researchers had begun studying Bayes 50 years earlier.

The heart of all the controversy had to do with the way Bayes began his search for an answer to the inverse probability problem. Probability theory was in its infancy in Bayes's time and, McGrayne writes, applied primarily to gambling: the odds of picking up four aces in three consecutive poker hands, for example, which you could describe as reasoning from cause to effect. The inverse problem instead sought to reason from effect to cause: if you had three consecutive poker hands of four aces, what is the underlying chance that the deck is loaded?

Bayes' notion was to start the solution to such problems with a guess and then use further data to refine the guess, narrowing the range of his answer over time and increasing his confidence in it (that is, the probability that it was correct). What offended two centuries of critics was first the notion of an initial guess, which seemed too subjective, and second that Bayes was willing to assign equal probability for certain types of data. Both of these, McGrayne writes, are now accepted as reasonable ways to work with uncertainty. His ideas were taken up after his death by his friend Richard Price, and then further developed by Pierre Simon Laplace. And today they are everywhere. If Bayes could wake up for one day, he'd be astounded at his impact on the world.

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy
By Sharon Bertsch McGrayne
Yale University Press
320 pages
ISBN: 978-0-300-16969-0
£18.99